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␈↓ ↓H␈↓␈↓ ∧∨␈↓∧␈↓&Automated Math Theory Formation␈↓)αβ␈↓

␈↓ ↓H␈↓␈↓ ¬m␈↓↓Douglas B. Lenat␈↓
␈↓ ↓H␈↓␈↓ ¬;Arti≡cial Intelligence Lab
␈↓ ↓H␈↓␈↓ ¬←Stanford University
␈↓ ↓H␈↓␈↓ ¬2Stanford, California 94305






␈↓ ↓H␈↓␈↓ ¬:␈↓&Brief Summary of Thesis␈↓)αβ






␈↓ ↓H␈↓Investigations␈αof␈αcreative␈αtheory␈αformation␈αin␈αempirical␈αscience␈αhave␈αled␈αto␈αthe␈αconstruction␈αof␈αAM,␈α
a
␈↓ ↓H␈↓heuristic␈αsearch␈αprogram␈αwhich␈αcan␈αdo␈αsimple␈αmathematical␈αresearch.␈α AM␈αexamines␈α
empirical␈αdata,
␈↓ ↓H␈↓proposes␈αplausible␈αconjectures,␈αformulates␈αnew␈αde≡nitions,␈αand␈αjudges␈αthe␈αworth␈αof␈αeach␈αnew␈αconcept.
␈↓ ↓H␈↓AM's␈α
guiding␈α
heuristics␈α
are␈α
used␈α
as␈α
a␈α
rudimentary␈α
calculus␈α
to␈α
evaluate␈α
"interestingness".␈α Currently,
␈↓ ↓H␈↓AM␈α⊃is␈α⊃given␈α⊃prenumerical␈α⊂knowledge,␈α⊃and␈α⊃makes␈α⊃forays␈α⊂into␈α⊃arithmetic␈α⊃and␈α⊃elementary␈α⊂number
␈↓ ↓H␈↓theory.
␈↓ ↓H␈↓␈↓ ¬m␈↓↓Douglas B. Lenat␈↓
␈↓ ↓H␈↓␈↓ ¬;Arti≡cial Intelligence Lab
␈↓ ↓H␈↓␈↓ ¬←Stanford University
␈↓ ↓H␈↓␈↓ ¬2Stanford, California 94305






␈↓ ↓H␈↓␈↓ ∧3␈↓∧␈↓&Publications and work in progress␈↓)αβ␈↓





␈↓ ↓H␈↓Green,␈αC.␈αC.,␈α
R.␈αWaldinger,␈αD.␈αBarstow,␈α
R.␈αElschlager,␈αD.␈αLenat,␈α
B.␈αMcCune,␈αD.␈α
Shaw,␈αand
␈↓ ↓H␈↓␈↓ αHL.␈αSteinberg,␈α␈↓βProgress␈αReport␈αon␈αProgram-Understanding␈αSystems␈↓,␈αMemo␈α
AIM-240,
␈↓ ↓H␈↓␈↓ αHCS␈α"Report␈α"STAN-CS-74-444,␈α"Arti≡cial␈α"Intelligence␈α#Laboratory,␈α"Stanford
␈↓ ↓H␈↓␈↓ αHUniversity, August, 1974.


␈↓ ↓H␈↓Lenat,␈α∪D.␈α∪B.,␈α∪␈↓βSynthesis␈α∪of␈α∪Large␈α∪Programs␈α∪from␈α∪Speci≡c␈α∪Dialogues␈↓,␈α∪Proceedings␈α∪of␈α∪the
␈↓ ↓H␈↓␈↓ αHInternational␈α∃Symposium␈α⊗on␈α∃Proving␈α∃and␈α⊗Improving␈α∃Programs,␈α⊗Le␈α∃Chesnay,
␈↓ ↓H␈↓␈↓ αHFrance, sponsored by IRIA, July, 1975.


␈↓ ↓H␈↓Lenat,␈α⊃D.␈α∩B.,␈α⊃␈↓βDuplication␈α∩of␈α⊃Human␈α⊃Actions␈α∩by␈α⊃an␈α∩Interacting␈α⊃Community␈α∩of␈α⊃Knowledge
␈↓ ↓H␈↓β␈↓ αHModules␈↓,␈α∪Proceedings␈α∪of␈α∩the␈α∪Third␈α∪International␈α∩Congress␈α∪of␈α∪Cybernetics␈α∩and
␈↓ ↓H␈↓␈↓ αHSystems, Bucharest, Roumania, August, 1975.


␈↓ ↓H␈↓Lenat,␈α∃D.␈α∀B.,␈α∃␈↓βBEINGS:␈α∀Knowledge␈α∃as␈α∀Interacting␈α∃Experts␈↓,␈α∀Proceedings␈α∃of␈α∃the␈α∀Fourth
␈↓ ↓H␈↓␈↓ αHInternational␈α⊂Joint␈α⊂Conference␈α⊂on␈α⊂Arti≡cial␈α⊂Intelligence,␈α⊂Tbilisi,␈α⊂Georgia,␈α⊂USSR,
␈↓ ↓H␈↓␈↓ αHSeptember, 1975.


␈↓ ↓H␈↓Lenat, D. B., ␈↓βThe Automated Mathematician␈↓, (forthcoming ACM paper).
␈↓ ↓H␈↓␈↓ ¬m␈↓↓Douglas B. Lenat␈↓
␈↓ ↓H␈↓␈↓ ¬;Arti≡cial Intelligence Lab
␈↓ ↓H␈↓␈↓ ¬←Stanford University
␈↓ ↓H␈↓␈↓ ¬2Stanford, California 94305






␈↓ ↓H␈↓␈↓ ∧v␈↓∧␈↓&Plans for Future Research␈↓)αβ␈↓




␈↓ ↓H␈↓The␈α∩fascinating␈α∩task␈α∪of␈α∩understanding␈α∩and␈α∩automating␈α∪scienti≡c␈α∩theory␈α∩formation␈α∪will␈α∩probably
␈↓ ↓H␈↓occupy␈αmy␈αresearch␈αtime␈αfor␈αthe␈αnext␈αfew␈αyears.␈α Some␈αof␈αthe␈αprojects␈αI␈αam␈αcontemplating␈α
are␈αdirect
␈↓ ↓H␈↓outgrowths of AM, the "Automated Mathematician" project which is my dissertation.

␈↓ ↓H␈↓For␈α
example,␈α
attention␈α
should␈α
be␈α
paid␈α
to␈α
those␈α
mathematical␈α
discoveries␈α
which␈α
␈↓βcan't␈↓␈α∞be␈α
synthesized
␈↓ ↓H␈↓by␈αthe␈α
kind␈αof␈αheuristic␈α
procedure␈αAM␈αfollows;␈α
that␈αis,␈αwhat␈α
historical␈αinductive␈αleaps␈α
remain␈αwhen
␈↓ ↓H␈↓all the "hack" discoveries are discounted?

␈↓ ↓H␈↓Another␈α
possible␈α
direction␈α
for␈α
my␈α
work␈α
next␈α
year␈αis␈α
to␈α
take␈α
the␈α
≡rst␈α
step␈α
toward␈α
the␈α
codi≡cation␈αof␈α
the
␈↓ ↓H␈↓heuristics␈α∀necessary␈α∀for␈α∀creative␈α∀work␈α∀in␈α∀mathematics.␈α∀ The␈α∀AM␈α∀program␈α∀can␈α∀be␈α∀used␈α∀as␈α∪an
␈↓ ↓H␈↓experimental␈α∂instrument,␈α⊂to␈α∂help␈α⊂clarify␈α∂the␈α⊂role␈α∂of␈α⊂each␈α∂heuristic.␈α⊂ Ultimately,␈α∂such␈α⊂a␈α∂codi≡cation
␈↓ ↓H␈↓could␈αlead␈α
to␈αa␈αprogramme␈α
for␈αteaching␈αstudents␈α
how␈αto␈αdo␈α
creative␈αresearch.␈α If␈α
AM␈αcan␈α
do␈αuseful
␈↓ ↓H␈↓theory formation, then certainly so can bright students who have learned the same heuristics.

␈↓ ↓H␈↓An␈αorthogonal␈αresearch␈αinterest␈αof␈αmine␈αis␈αto␈αexpand␈αAM␈αto␈αdomains␈αother␈αthan␈αelementary␈αnumber
␈↓ ↓H␈↓theory.␈α
 Apparently,␈αthe␈α
harder␈αa␈α
science␈αis,␈α
the␈αmore␈α
appropriate␈αit␈α
is␈αto␈α
try␈αto␈α
automate␈αformation␈α
of
␈↓ ↓H␈↓its␈αtheories.␈α
 So␈αsome␈α
candidate␈αdomains␈αinclude␈α
geometry,␈αcryptography,␈α
calculus,␈αand␈α
algebra.␈α Still
␈↓ ↓H␈↓plausible␈α⊃are␈α⊃parts␈α⊃of␈α⊂chemistry␈α⊃and␈α⊃physics␈α⊃(e.g.,␈α⊃mechanics).␈α⊂ ␈↓βVery␈↓␈α⊃soft␈α⊃≡elds␈α⊃like␈α⊃sociology␈α⊂and
␈↓ ↓H␈↓psychology␈α∩have␈α∪primitive␈α∩concepts␈α∩which␈α∪are␈α∩just␈α∩too␈α∪slippery␈α∩to␈α∩deal␈α∪with␈α∩or␈α∪even␈α∩represent
␈↓ ↓H␈↓adequately using the ideas AM is based on.

␈↓ ↓H␈↓Periodically,␈α∞I␈α∞will␈α∞return␈α
to␈α∞the␈α∞general␈α∞problem␈α∞of␈α
theory␈α∞formation,␈α∞and␈α∞analyze␈α∞the␈α
information
␈↓ ↓H␈↓gleaned␈αfrom␈αmy␈α
experimental␈αsystems.␈α This␈αmight␈α
result␈αin␈αa␈α
list␈αof␈αgeneral-purpose␈αheuristics,␈α
some
␈↓ ↓H␈↓notion␈α
about␈α
how␈α
best␈α
to␈α∞proceed␈α
to␈α
uncover␈α
valuable␈α
new␈α
ideas,␈α∞or␈α
some␈α
handles␈α
on␈α
how␈α∞to␈α
more
␈↓ ↓H␈↓e≥ectively␈αformalize␈αinductive␈αheuristics␈αinto␈αa␈αprogram.␈αI␈αbelieve␈αthat␈αwe␈αcan␈αlearn␈αmuch␈αmore␈αfrom
␈↓ ↓H␈↓studying (and trying to emulate) problem-␈↓βproposing␈↓ tasks rather than from problem-solving tasks.